\(\mathcal {A}\) -distance. Based on the theory of Ben-David et al. [1]}, \(\mathcal {A}\) -distance is used as a metric for the domain discrepancy, where a smaller \(\mathcal {A}\) -distance might indicate better DA performance. Generally, the \(\mathcal {A}\) -distance is computed as \(d_{\mathcal {A}} = 2(1-2\epsilon )\) , where \(\epsilon \)  is the generalization error of a classifier trained with the binary classification task of discriminating the source and target. In the adversarial training framework, we can just keep \(D\)  as such a classifier. The comparative results are shown in Fig. REF . From this figure, we can see that the introduction of IB / SIB significantly reduces \(\mathcal {A}\) -distances compared to the baseline. However, we can also observe that the \(\mathcal {A}\) -distance of IBAN is slightly smaller then SIBAN. Consistent with our previous analysis on training stability, we conclude that the discrepancy decrease of IB is at the cost of discarding some necessary information. This finding tells us that only reducing the global distribution discrepancy is far from enough for domain adaptation. The superior DA performance, as well as a relatively small \(\mathcal {A}\) -distance lead by SIBAN, show that our method can make a better trade-off between the feature purification and domain alignment.
